“We’ve heard again the contradictory message of protecting Ireland, the Good Friday Agreement, no hardening of the border, but yet a determination to leave the single market and the customs union and to take the north with them.”

Mrs McDonald said everything they heard in the meeting adds to their worries, rather than relieving their concerns.

“The British now wish to leapfrog, set aside, disregard, the Irish question, to pursue their own interests in respect of a new relationship that they may wish to craft.

“That is very dangerous for Ireland. That is unacceptable,” she said.

Mrs McDonald said she expects Irish leaders and their EU partners will make that absolutely clear to Mrs May and the UK Government.

Speaking earlier, Mrs McDonald said: “We are here because Brexit poses a real and imminent danger to Irish interests both north and south.

We are here because the British system so far has failed to come up with a credible proposal that would protect the Good Friday Agreement
Mary Lou McDonald, Sinn Fein president

“We are here because the British system so far has failed to come up with a credible proposal that would protect the Good Friday Agreement, that would prevent a hardening of the border and would protect citizens’ rights.

“Despite all of the rhetoric Theresa May has drawn a blank by way of response to those issues, so we believe that there’s game playing, there’s brinksmanship and that the Tory Government are playing a game of chicken with Brexit and with Ireland. We find that unacceptable,” she said.

Her comments come amid an ongoing impasse between the EU and UK on how to avoid a hard border post-Brexit.

Both sides have agreed to include a so-called backstop option in the withdrawal treaty. The measure would commit the UK to align with an EU regulatory framework in the absence of a wider trade deal.

But the shape of that fall-back remains a sticking point, with the EU dismissing the UK suggestion it should be a temporary arrangement, even if a broader agreement fails to materialise.

Mrs McDonald reiterated Sinn Fein’s call for the Prime Minister to grant Northern Ireland special status, allowing it to remain in the customs union and the single market.

Mrs McDonald added: “The British Government know what the answer is. They know precisely what the answer is but they’re playing games and I think certainly patience has run out with that approach. It’s dangerous, it’s reckless.”

During their visit to London the powersharing impasse was also on the agenda.

Both Mrs McDonald and Mrs O’Neill blamed the stalemate between the Sinn Fein and the DUP on the Unionists’ coalition with the Tories since last summer’s general election.

“The DUP have gone into hiding – they have a very toxic relationship under Theresa May’s wing,” said Mrs McDonald.

Mrs O’Neill added: “This political vacuum has been allowed because of this relationship and is all about trying to keep the Tories in power at the expense of government in the north of Ireland.

“It’s not acceptable. The British Government need to step up and play their role as co-guarantors of our peace process.

“They need to step up and deliver rights that are available elsewhere to other citizens here whether that be marriage equality or language rights – all things that are freely available across these islands but not to people in the north.

“We are being treated as this little backwater area where we can’t get our rights and we’re being denied economic prosperity because of Brexit.

“It’s just not a tolerable situation so that’s the message we would bring loud and clear to Theresa May today.”

They (Sinn Fein) sit on the outside as spectators dependent on others to get decisions made
Nigel Dodds, DUP deputy leader